What are the divisors of 869?
1, 11, 79, 869
- There is a total of 4 positive divisors.
- The sum of these divisors is 960.
- The arithmetic mean is 240.
4 odd divisors
1, 11, 79, 869
How to compute the divisors of 869?
A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.
Brute force algorithm
We could start by using a brute-force method which would involve dividing 869 by each of the numbers from 1 to 869 to determine which ones have a remainder equal to 0.
(where is the integer part of the quotient)
- 869 / 1 = 869 (the remainder is 0, so 1 is a divisor of 869)
- 869 / 2 = 434.5 (the remainder is 1, so 2 is not a divisor of 869)
- 869 / 3 = 289.66666666667 (the remainder is 2, so 3 is not a divisor of 869)
- ...
- 869 / 868 = 1.0011520737327 (the remainder is 1, so 868 is not a divisor of 869)
- 869 / 869 = 1 (the remainder is 0, so 869 is a divisor of 869)
Improved algorithm using square-root
However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 869 (i.e. 29.478805945967). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:
(thus, if , then )
- 869 / 1 = 869 (the remainder is 0, so 1 and 869 are divisors of 869)
- 869 / 2 = 434.5 (the remainder is 1, so 2 is not a divisor of 869)
- 869 / 3 = 289.66666666667 (the remainder is 2, so 3 is not a divisor of 869)
- ...
- 869 / 28 = 31.035714285714 (the remainder is 1, so 28 is not a divisor of 869)
- 869 / 29 = 29.965517241379 (the remainder is 28, so 29 is not a divisor of 869)